Creating a curved rectangle on outside of a sphere?
It sounds like you want to do something like this:

To model that:

Add a plane (ShiftA &gt; Add &gt; Mesh &gt; Plane).

Give it some extra geometry with a Simple Subdivision surface modifier:


Add a shrink wrap modifier and select the target object in the Target input box:


Add a Solidify modifier to give it some thickness:



And you get: